initial text of articleSome first impressions of the
Kinship Network
Three features of the graph are striking: (1) The 26 shortest elementary cycles are long; none are short; (2) Families do not cluster in the center but are spread out along the edges in cycles of very large diameter or as points connected to the cycles; (3) The families of economic rank 1 and 3 tend to occur more frequently in the cycles of the graph while 2 and 4 are more common in the peripheries of the graph. The next inset is a view of this structure from the top, and shows the relative emptyness of the center given the lack of short cycles.

Click for detail and larger Image

Note the contrast with the following inset, a graph of the compadrazgo network, which is drawn with the same spring embedding algorithm but has a starkly higher concentration of short cycles in the center of the graph.

Some first impressions of the
Compadrazgo Network

Click for larger Image
(39K)

The colors mark different structural
positions in the
network

People who live in Belen and
are connected to the largest relinked block.

People who live in Belen
and are NOT connected to the largest relinked block.

People from outside Belen
who are integrated in the largest relinked block.

People from outside Belen
who are NOT relinked.

Here is the Frequency distribution of the different
patterns:

Pattern

Freq.

Percent

113

8,6

29

2,2

1028

78,5

140

10,7

From this classification of people a classification
of links can be generated. There are for example links the well integrated
Belenos (yellow) have to the not integrated outside world (red). Those links
are likely to different from the links - let's say - the well integrated
Belenos have to other well integrated Belenos (links from yellow to yellow).
The general question is whether links that are structurally different differ
also in other matters.

In the classification we find seven different
patterns:

Classification

Freq.

Percent

381

7

1436

502

7

118

50

15,2

,3

57,4

20,1

,3

4,7

2,0

For a first analysis those patterns will be
combined to only three. These are the tree like ties that link to the outside
world (3 and 6), those that link to the outside but integrated non Belen
community (4 and 7) and links that stay within Belen ( 1, 2, and
5)

A first question would be through what kinds
of compadrazgo those structurally different links are established. Here is
a the raw data:

Type of Compadrazgo

Tree like links to the
outside

Ties to Belenos

Ties to "integrated"
outsiders

101

102

103

104

105

106

107

108

109

110

111

112

113

114

116

117

119

120

121

122

123

126

127

128

131

132

208

501

502

503

504

505

506

507

508

509

510

511

512

513

514

516

517

519

520

521

522

523

526

527

528

529

530

531

532

437

260

155

44

4

8

8

15

9

11

9

1

3

2

4

9

29

4

1

1

8

4

6

0

0

0

0

181

141

29

35

7

10

5

17

5

15

3

3

7

3

4

11

22

4

1

1

1

1

9

4

0

1

0

2

54

26

40

1

7

13

9

10

9

8

1

0

4

1

2

2

7

0

1

0

3

1

0

3

0

1

0

39

11

26

3

4

11

5

8

9

11

1

1

4

3

2

3

20

0

0

1

1

0

0

15

7

4

2

1

159

110

42

37

4

7

3

11

9

4

1

0

7

0

0

2

6

0

0

0

0

3

3

3

1

1

1

23

19

15

14

4

4

4

4

4

4

1

0

3

2

0

3

6

0

0

0

0

3

6

8

3

5

3

0

Correspondence Analysis helps to make some of
the structural patterns visible. Since the matrix rank is 2 we have a perfect
fit in two dimensions (60% variance on the first eigenvalue which means
that you primarily need to look at that
dimension).

Here are the
results:

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(10K)

The red dots are
the sacramental compadrazgos. The analysis clearly shows that the most important
relationships are the tree like ends of the networks. These important
relationships are clearly not established within the community
nor within the redundant block that surrounds the community. The explanation
is pretty strait forward: the structurally weakest ties (the
dead ends) become the highest symbolic or cultural emphasis. Another argument
would be that people try to integrate far away but potentially important
people in their personal
network.

In which regions do those structurally
different ties reach

Code

Name of Place

Integrated ties

Percent

Tree like ties

Percent

22

21

101

348

23

51

181

341

630

12

462

362

241

403

404

24

142

361

401

431

311

452

100

312

381

237

437

Belen

San Bernabe

Santa Ana Chiautempan

Acxotla del Rio

San Matias

Apizaco

Contla

Tlaxcala

Mexico D.F

San Damian

Puebla

Los Reyes

Pontla

San Lucas

San Simon

Tecolotla

San Simeon

Toluca

Xalostoc

Yauhquemehcan

Terrenate

Altixo

Santa Elena

Tenayucan

Tzompantepec

.not in code

Santa Ursula

186

61

58

30

28

18

14

14

13

10

9

9

8

0

0

0

0

0

0

0

0

0

0

0

0

0

0

26,6

50,4

24,4

66,7

31,5

31,6

11

20,6

11

24,4

12

81,8

42,1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

119

60

180

15

61

39

113

54

105

31

66

2

11

25

25

17

16

16

16

16

10

10

9

9

9

8

8

17

49,6

75,6

33,3

68,5

68,4

89

79,4

89

75,6

88

18,2

57,9

100

100

100

100

100

100

100

100

100

100

100

100

100

100

There is a general tendency that most of the
integrated ties stay closer (in physical terms). Some cases are interesting
and ask for an ethnographic
explanation.

1) Why is it that Acxotla del Rio and Los Reyes
are so well integrated? Acxotla is a town on the highway from Belen that
is the edge of the capital of Tlaxcala and is the "urban settlement" for
Belenos; Los Reyes is nearby and a bit further from the
city.

2) The tree like relationships go Tlaxcala,
Puebla, Mexico D.F, Contla, Santa Ana Chiautempan, Apizago andSan Matias. Tlaxcala and Mexico D.F. are the
state and national capitals, Puebla the capital of the neighboring state,
Contla is the regional weaving industry, Santa Ana and Apizaco the nearest
market towns, and San Matias the next village along the highway in the direction
of Santa Ana and Tlaxcala city.

3) What is the difference between San Bernabe
and Santa Ana Chiautempan? San Bernabe is a neighboring village similar
to Belen; Santa Ana the closest market town.

Ties and occupations

Do people with different occupations have different
patterns of ties? And if yes - is there any change over time?. The following
analysis shows how the proportion of ties that goes in the relinked block
has developed over the last years.

(click for larger image
90K)

The analysis shows that there was an overall
peak in the late 50s and 60s where many relationships were invested into
relinked ties. Thought that pattern is not the same for all occupations:
the labradores show a very stable pattern, some others (like the
oficios corrientes invest more ties in the relinked structure than
in tree like relationships to the outside. If we look at the picture only
from the latest point in time there are some differences in how much the
group spends in the community.

Social Class and Stratification

Which role does the economic rank of the two
compadres play for the establishment of the relationship? In theory we can
distinguish at least three different systems: a class system,
where almost all relationships are within ones social and economic class,
an egalitarian system, where the economic position is not reflected in the
social relationships and a patronage system, where wealth differences can
be expected to be very high. Let us take a look, which model fits best to
the compadrazgo data the relationships within Belen? Here
is the matrix of relationships:

To understand more about the relationship between
the four economic groups it helps to convert the matrix into a vector of
distances between the groups. The distance between the "very rich" and the
"very poor" can be defined as 1 - 4 = -3. The other way around the distance
would be 4 - 1 = 3. This way we keep the asymmetry of the
relationships.The results look
like this:

How to read the table? The zero in the middle
are all the relationships that are along the diagonal. If we were looking
at a class system most of the relationships should concentrate here. This
is not the case. In an egalitarian system all relationships should be equally
distributed. This is not the case as well. What we find is that most
relationships are one step below or above the class one belongs to, and these
relationships are the only ones with higher than expected frequencies.
In addition, there are more relationships that go up the economic ladder
than there are relationships that go down.

But who is it that establishes those relationships?
Is there any pattern here? Let us move a step further and consider which
of the relationships in the matrix above are stronger than would be expected
by chance. This statistical logic might uncover some of the patterns in the
matrix.Here are the results:

(click for larger image 5K )

The diagram shows all the relationships from
the above matrix that are larger than would be expected from the row and
column distributions. The first number on the arrow gives the number of
relationships and the value in brackets indicates how much it is above the
expected value. The direction of the arrow indicates who asked
whom. For the interpretation one needs to keep in
mind that these are only the relationships within Belen. The picture would
lead to the following simplfication:

ask someone from one class below your own.

if you are in the lowest class, ask someone
from one class above.

the arrow from the 3. class to the 1 one needs
an interpretation (any idea - doug ???).

Only because there is not much relinking in the elite does that mean that the elite does not have a special structural position?

As it looks it does not. The above
table gives the mean results from betweenness centrality measures
for each of the four groups. The results clearly indicate that centrality
in the system declines with the economic rank of the actor. The elite does
not "close up" by high internal integration but becomes an integrated
center of the network. This might be a somewhat typical situation
for a community that is in a transition stage. No class but structural
stratification.